Rough wall effect on micro-swimmers. (English) Zbl 1315.93015
Summary: We study the effect of a rough wall on the controllability of micro-swimmers made of several balls linked by thin jacks: the so-called 3-sphere and 4-sphere swimmers. Our work completes the previous work of F. Alouges, L. Giraldi [”Enhanced controllability of low Reynolds number swimmers in the presence of a wall”, Acta Appl. Math. 128, No. 1, 153-179 (2013; Zbl 1287.35063)] dedicated to the effect of a flat wall. We show that a controllable swimmer (the 4-sphere swimmer) is not impacted by the roughness. On the contrary, we show that the roughness changes the dynamics of the 3-sphere swimmer, so that it can reach any direction almost everywhere.
MSC:
| 93B05 | Controllability |
| 35Q93 | PDEs in connection with control and optimization |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Keywords:
low-Reynolds number swimming; self-propulsion; three-sphere swimmer; rough wall effect; Lie brackets; control theory; asymptotic expansionCitations:
Zbl 1287.35063References:
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